Question

Solve 2tan^2 x + tanx - 3 = 0

Answer 1

Ok lets start off with subsituting x=tanx

Answer 2

\[2x^2+x-3=0\]
Now we have a quadratic equation and we must solve for x

Answer 3

(2tan+3)(tan-1)=0

Answer 4

\[2x^2-2x+3x-3=0\]
\[2x(x-1)+3(x-1)=0\]
\[(2x+3)(x-1)=0\]
\[ x= - \frac{3}{2} \text{ and }x=1\]

Answer 5

Now let us plug tan x back into our equation
\[\tan x= - \frac{3}{2} \text { and } \tan x=1\]
\[ x= \tan^{-1}(- \frac{3}{2}) \text { and } x=\tan^{-1}(1)\]

Answer 6

@christen_j0 Im leaving the rest for you to solve